By "introduce", I mean the entire "sponsorship" process, up to the point where it is given to the House and Senate for discussion/votes.
Is there any given reason why a citizen can't write a bill and present it to Congress themselves?
Has this rule been in effect for the entirety of the U.S.'s history? If not, where did it originate and what was the reasoning behind it?
It's Article I, Section I of the U.S. Constitution:
All legislative Powers herein granted shall be vested in a Congress of the United States, which shall consist of a Senate and House of Representatives.
Legislative powers are the ability to create and introduce new laws. Vested means that they are fully controlled by the Congress. So private citizens cannot introduce new legislation to Congress unless they can first get a Representative or Senator to sponsor (introduce) the bill to Congress.
The reasoning is that if a bill has so little merit that not even one legislator can be bothered to sponsor it, then it has no chance of passing anyway.